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In a polynomial p(x) = 2x^3 + 9x^2 + kx + 3, p(-2) = p(-3). Find the value of k.

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In a polynomial p(x) = 2x3 + 9x2 + kx + 3, p(-2) = p(-3). Find the value of k.

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p(x) = 2x3 + 9x2 + kx + 3

p(-2) = 2(-2)3 + 9(-2)2 + k(-2) + 3

= -16 + 36 – 2k + 3 = 23 – 2k

p(-3) = 2(-3)3 + 9(-3)2 + k(-3) + 3

= -54 + 81 – 3k + 3 = 30 – 3k

We have p(-2) = p(-3),

23 -2k = 30 -3k

-2k + 3k = 30 – 23

k = 7

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